As mentioned before, you must have all other eight Dragon Priest Masks first before obtaining Konahrik. After having them all, you need to place them on a Shrine inside Labyrinthian.

You do not need to enter the giant maze-like ruin! Look for a small dome structure on the outside, in the snow. Inside the dome is a skeleton, a note, and a wooden mask. Put the mask on to travel back in time to when the Dragon Priest Mask was still in good shape. Place all your masks, except for the wooden mask, on the shrine to receive the ninth mask. Take off the wooden mask to go back to present day.

WARNING: It's been said your Dragon Priest Masks will revert to the original status when you pick them back up, instead of being upgraded if you did upgrade it via Smithing.